Question

Assertion : When the displacement of a body is directly proportional to the square of the time, then the body is moving with uniform acceleration. Reason : The slope of velocity-time graph with time axis gives acceleration.​

Answer 1

Answer:

Both assertion and reason are correct but reason is not the correct explanation of assertion.

Explanation:

When displacement of body is given by

${t}^{2}$

So differentiating t^2 with respect to dt will result 'v' as 2t.

Now again differentiating v with respect to dt we get 'a' as 2.

Hence the body will have zero acceleration as the value of 'a' is constant

Answer 2

Both assertion and reason are true but reason is not correct explanation for assertion.

Explanation:

• Kinematics equations refer to uniform accelerated motion. Acceleration is considered to remain constant when applying kinematics equations.

• When an object start its motion with initial velocity $u$ to cover displacement $s$ in time $t$ with final velocity $v$ in a uniform accelerated motion with acceleration $a$.
• Then the kinematics equations are:

$v=u+at\\s=ut+\frac{1}{2} at^{2} \\v^{2} =u^{2} +2as$

• From second equation of motion, it can be derived that displacement is directly proportional to square of the time.

• Acceleration is defined as rate of change of velocity with time:

$a=\frac{v-u}{t}$

So, slope of velocity-time graph gives acceleration.